Conventionally, there has been the following problem: in a low-temperature polymerization reaction of an olefin compound, cooling energy necessary for cooling of a raw material liquid subjected to the reaction and cooling of the inside of a reactor during the reaction is large. In response to this problem, Patent Literature 1 describes a method for producing an isobutylene-based polymer, characterized in that a raw material liquid to be fed to a reactor is cooled in advance by heat exchange with a reaction liquid discharged.